Speaking from Kupang in Indonesia, two men from two separate journeys have described their experiences to the media for the first time. Though difficult to verify, both men's stories are strikingly similar.

One man named Yusuf identified himself as a Sudanese asylum seeker, and says he and his wife paid $6,000 to travel from Indonesia to Australia.

They boarded a boat with more than 40 others, and reached a small island off the coast of Darwin before the engine broke down on New Year's Day.

Yusuf says after the group called the United Nations for help, two Australian naval ships arrived.

Key points

Two men claim they were on boats towed back to Indonesia

Their claims are difficult to verify

One of the men says the Navy used force on the asylum seekers

He says they were denied food and told they were being taken to Christmas Island

He says they were abandoned at sea after the five-day tow back

The second man tells a similar story, and claims asylum seekers were "punched"

The Government has declined to comment on the "operational" matter

The ship numbers he gave correlate to those for HMAS Parramatta and HMAS Glenelg.

Yusuf says the Navy used force on some people, including women, while transferring them to one of the Navy boats.

Yusuf says a number of people were restrained, and that some of the people on board jumped into the water.

"Some of our people, they jump on the water as a protest. Nine people, and then they take them aboard," he said.

It was the start of a tow-back that was to last five days.

Yusuf says those on board were told they were being taken to Christmas Island, denied their satellite and navigation tools and given just one meal a day.

He claims the Navy fixed one of the boat's engines before the asylum seekers were forced back onto their boat.

He says the Navy then abandoned the group in the middle of the night in rough seas off Indonesia's Rote Island.

Mr Morrison did however comment on claims Yusuf made about four people falling overboard before Australian authorities arrived.

"In relation to reports of claims that four people may have fallen overboard from a suspected illegal entry vessel inside Australian waters, I am advised that these claims were acted on and rigorously assessed at the time they were made and were deemed to be false," he said.

"This assessment included close questioning of all people on board the vessel, including the Master of the vessel who indicated that no-one had fallen overboard.

"It is important to note that the claimed incident occurred well before the suspected illegal entry vessel had been intercepted by Australian authorities."

Greens Senator Sarah Hanson-Young says Mr Morrison should not be picking and choosing what he wants to verify.

"He needs to be up front with the Australian people, up front with how these operations are occurring on the high seas and if anything he's given more credence to the fact that these types of dangerous operations are happening more frequently than we realise," she said.